id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-2118	Tunc, Tuncay; Åžimsek, Ersin	Some Approximation Properties of Szasz-Mirakyan-Bernstein Operators	2014	10	.pdf	application/pdf	3538	185	83	[0,1], that � �En � f ; x � − f (x) � �≤ En �� � f − f (x) � � ; x � . (8) Now using (5) in inequality (8) we have, for any δ > 0, that � �En � f ; x � − f (x) � �≤ � 1+ 1 δ En �� �e1 − x � � ; x � � ω � f ;δ � (9) Applying the Cauchy-Schwartz inequality for positive linear operators it follows from (9) that � �En � f ; x � − f (x) � �≤ � 1+ 1 δ r En � � e1 − x �2 ; x � � ω � f ;δ � Using Lemma 1 in the last inequality, we can write � �En � f ; x � − f (x) � �≤  1+ 1 δ � (1− x) � 1− e−nx � nαn �1/2  ω � f ;δ � ≤ 1+ 1 δ � 1 nαn �1/2 !	cache/ejpam-2118.pdf	txt/ejpam-2118.txt